Maybe you found this blog while searching for texts related to physics, maths and/or one of the scientists named Bernoulli. Though, every now and then, I might write about maths, the main scope concerns the world of chess problems - views, experiences, pleasures, moments of frustration (indeed!). In most cases, posts are about solving, constructing, enjoying chess compositions.

27 May 2011

I dug out another book by T. R. Dawson. This time, it's C. M. Fox, His Problems, published in 1936. As one might correctly guess, it's a collection of the best problems composed by Charles Masson Fox.

After many years as chess player, Fox took to fairy chess in 1921-22 and his very first published problem won a first prize. What a start! He became a renowned fairy chess expert.

I selected his "coal box" family from the book. Dawson was sure that it's "never likely to be forgotten by any solvers". He further explicates: "The problems in it are some of his earliest efforts in 1921, but they show him extracting ideas one from another in his most familiar style. The general idea is to fix the black king at g6, surround him with heavy artillery, and lead the White infantry to a successful assault. In some cases the enemy forces zig-zag round their king; in others the latter attempts flight from his encampment only to fall into worse hands. Besides choice of mating square — the black king gets a wide range — there is a wealth of delicate timing, surprising loss of a white pawn sometimes, Black interferences including critical moves, and a fair choice of mating "pictures" — and it is all done with the most deceptive appearance of ease."

All problems have the same stipulation: helpmate in 3 moves. All of them were published in The Problemist Fairy Chess Supplement, October 1932. Just in order to save space, only the relevant right part of the board is shown. If you rather prefer to see the whole board, you may click on the respective diagram.

20 May 2011

Another very interesting little book on fairy chess by Thomas Rayner Dawson is Caissa's Wild Roses (published 1935). As the author states in his preface, this was "the first English text to give a reasonably broad outline of Fairy Chess".

The booklet starts with some remarks about the term fairy chess in comparison to normal chess. What are the characteristics of normal chess? Firstly, you have the playing space. It is a plane board with eight ranks and eight files. Secondly, there are the six different types of pieces: king, queen, rook, bishop, knight, and pawn. Each of them has its own style of moving. Thirdly, miscellaneous limitations on move freedom exist, e.g. the alternation of White and Black moves, capture, pawn promotion, castling, check, checkmate, various types of draws. Dawson concludes: "From this point of view, normal chess is evidently an arbitrary group of elements selected from an infinity of analogous geometrical conceptions. Fairy Chess comprises the study of all such elements, taken in arbitrary groups at will."

If you wanted to be absolutely correct and take the strictly formal approach, you'd have to define and list all elements of the respective fairy chess field that is relevant for a particular chess problem. Of course, there is a better way of handling that. The elements of the normal chess are considered as a basis and only the changes are mentioned. For instance, you use a new set of rules, leaving the board and the piece types unchanged. Or you might introduce a new type of piece and only modify the normal rules where necessary.

Dawson ends his comments on fairy chess with the following statement as one of the answers to the question why it finds enthusiastic devotees: "Fairy Chess offers an infinite field for the expression of Man's scientific and artistic imagination and adds new glory to his intellectual achievements."

In an earlier post featuring a larger board, I already mentioned the necessity of using a different board depending on the demonstrated theme, for instance. Interestingly, you can read something similar in Dawson's booklet: "The rational principles in studying chess boards as elements for variation are (i) the size of the board must be in unity with the problem representation; and (ii) the specific nature of each board demands the discovery of specific themes peculiar to such board (Problemist, March, 1928)."

The first example I picked for you shows a board with changing width in each phase, leading to different play, of course. Also, the problems 3 and 4 use a non-standard board. More of interest, though, is the concept of zig-zags featured in Nos. 2—4. Dawson himself admits that it is almost impossible to exactly define this term, as it rather covers a type of play than a type of problem (emphasis added by me): "The zig-zag involves the permutation of men of one or both colours, in general with abandonment of the principle of alternate White and Black moves, but not necessarily so." By the way, in one of my previous posts, I already showed an example of a zig-zag. Finally, you get to see three problems introducing illegal clusters. An illegal cluster is an illegal position which becomes legal upon removal of a single (arbitrary) unit, excluding kings.

1

T. R. Dawson

The Problemist, 1930

#2

(10+7)

inaccessible squares a1 to a6

a) Diagram

b) cut off h-file

c) further cut off g-file

d) further cut off f-file

e) further cut off e-file

f) further cut off d-file

2

T. R. Dawson

Eskilstuna.Kuriren, 1921

After every move all 4 men must
be guarded. Interchange rooks, with bishops back, in 28

3

T. R. Dawson

Bolton Football Field, 1910

No man ever guarding another, play 21. Ka4

4

T. R. Dawson

L'Eco degli Scacchi, 1918

No man ever guarding another, play 22. Ka4

5

T. R. Dawson

The Problemist Fairy Chess Supplement, 1933

Add black rook and black bishop to form an illegal cluster.

6

T. R. Dawson

The Problemist Fairy Chess Supplement, 1933

Add
a) two
b) three
black pawns to form an illegal cluster.

7

T. R. Dawson

The Problemist Fairy Chess Supplement, 1933

Add black rook and
a) one
b) two
black pawn(s) to form an illegal cluster.
c) like b) with position rotated
by 180 degrees

13 May 2011

As you know, in the world of chess problems, there are lots of basic themes. One of them is the Allumwandlung that you've already seen in several examples shown in my blog posts. Usually, a composer is demonstrating one or more themes in a chess problem. Normally, this is done on purpose. But sometimes, the composition has more richness than originally perceived or even intended.

Anyway, the more compositions there are, the bigger the challenge to come up with something new. The invention of a new theme might still be possible, yet it's quite rare. You can rather see that existing themes are varied and/or combined.

In his booklet Caissa's Wild Roses in Clusters (published 1937), Thomas Rayner Dawson discusses the field of theme transformations often making use of fairy chess elements. I've selected some "big" problems for you. Enjoy! Please bear in mind that only the thematic variations are mentioned.

The first three examples deal with the Grimshaw theme, named after the 19th century problem composer Walter Grimshaw. A Grimshaw denotes the mutual interference of two different types of pieces of the same colour arriving on a particular square. By the way, the referenced Wikipedia article wrongly states that a Grimshaw only deals with Black interferences, but there are also white Grimshaws! Anyway, it features some nice orthodox problems.

Each of the thematic black pieces observes a certain square in order to defend against a checkmate by the Nq3. The defenses are Nl1-i7, Bm1-c9 and Rh3xq3. The Grimshaw interference on k3 deactivates two of these moves, so that the white rook can take care of the third and deliver a discovered mate.

The three parallel lines of the nightriders (a15-h1, b14-f6, c13-g5) are cut by the three parallel lines of the queen and the two bishops (a14-e10, b12-f8, c10-g6) and vice versa. Dawson calls this a polylinear Grimshaw.

The aim of the Black defenses is to get a flight for his king. Moving to c10, Black unguards e10, the interference on c12 unguards f12 and playing a piece to g14 unguards g11. White answers by firing the three batteries Re2/Ne3, Rf8/Nf15 and Bo19/Nn18, respectively, corresponding to the flights. There's just the last variation whithout a battery firing, too bad.

The last two problems demonstrate the maximum mates by a grasshopper and a nightrider, respectively.

06 May 2011

Today, I'll take you on a short tour through a little book by Thomas Rayner Dawson called Caissa's Fairy Tales (published 1947). It's a loose collection of fairy chess problems embedded in fictional stories. Thereby, the reader becomes acquainted with certain types of fairy elements in an entertaining way. I chose three topics for you.

The first two diagrams are not really fairy problems. They simply add a constraint teasing the solver with a wordplay.

1

T. R. Dawson

Caissa's Fairy Tales, 1947

#3 with knight

(5+4)

2

T. R. Dawson

L'Eco degli Scacci, 1918

#3 with THE queen

(8+8)

In No. 1 it'd be easy to mate in three moves promoting one of the pawns to queen or rook. But it demands to mate with a knight. This should be accomplished using the one on c5, right? Let's see ...1. d7! puts Black in zugzwang:1. - Ne~ 2. Nc7+ Kb8 3. N5a6#1. - Ne6 2. Nxe6 3. Nec7# So far, Nc5 mates as expected.1. - Nxd7 2. Nxd7 3. Nc7# Oh, the Na6 also mates!1. - Nf~ 2. dxe8=N 3. Nec7# Ha, mate can also be delivered by this knight!

Problem No. 2 suggests the queen c6 is to give mate. Hmmm ...1. Qg6! c6,5 2. Ne6 ~ 3. Qxg5# Good, that works. But the black knight can spoil this idea.1. - Nh6 2. Qxg5+ What's that? Don't we need that queen? Kxg5 3. d8=Q# As there is only one white queen in the set, it is still THE queen!1. - N~ 2. Qxh5+ Kxh5 3. h8=Q# Again, THE queen.

The next two problems deal with the retraction of a move. Of course, only legal last moves can be retracted. And you have to choose the right retraction for White so that there is the possibility to mate in one.

3

T. R. Dawson

De Standaard, 1925

White retracts and mates in 1 (2+15)

a) Diagram

b) Bf4 → f6

c) further Pb7 → f2

4

T. R. Dawson

Eskilstuna Kuriren, 1933

Whatever Black retracts, White may retract and mate in 1 (12+10)

In No. 3 White could mate immediately with 1. Kg4#. However, the stipulation demands to retract a move, first.
a) Retract Kh4-h3 and play 1. Kg4#. Only the Bc8 is missing and it was captured at home. So, the white king did not capture on h3. Retraction of Kh2-h3 is not allowed, as the black pawn started on c7. Thus, the check on g3 would have been illegal.
b) Retract Kh2-h3 and play 1. Kgl# Analogous to a), Kh4-h3 is not allowed. Pawn g5 started on e7. On the other hand, the check on g3 is legal now, due to the possibility of f4xg3+.
c) Though Kh2-h3 could be retracted, it would be of no use. The white king could not leave the h-file. But the black bishop from c8 is now available for a capture. Retract Kg4xBh3 and play 1. Rxh3#.

Looking at No. 4, we quickly see that there is just a limited set of moves that Black can retract at all. It was the black pawn on f5 that made the last move. There are four possibilities and they remind of the Pickaninny theme (a problem in which a black pawn on its starting square makes each of its four possible moves).

Retract e6xRf5, Rf7-f5, then 1. Rc7#

Retract g6xRf5, Rg5-f5, then 1. Rxg3#

Retract f6-f5, Qgl-al, then 1. Qd4#

Retract f7-f5, Nc7-a6, then 1. Nd5#

Black cannot retract the capture of a bishop or a pawn on f5. In both cases, this would require too many captures by the white pawns. A capture of a knight or a queen is possible, though. The white pawn d2 could have promoted on d8 without a problem. In theses cases, the solution is not unique.

The last three problems feature a new type of fairy piece — the neutral men. Those can be moved by either side. Neutral pawns promote to neutral pieces on the first or on the eighth rank. The pieces are often shown by half white and half black symbols.
In 1912, Dawson invented the neutral pieces. Until his death in 1951, only 20 chess problems were composed using neutral men, 13 of them were by Dawson himself. Later on, these new pieces became highly popular.

No. 7 is a zugzwang problem:1. Qh4! and now1. - exd4 / nRh7,xh8 2. nRxf5#
1. - f4 2. nRxe5#
1. - Qxh8 / B~ 2. nRgxg6#
1. - Rxh6 2. nRxg7#
The key move creates a Q + nR battery. But, unlike a normal battery, it can only fire effectively when the neutral rook pins itself. Otherwise, Black would defend with 2. - nRg5.
In move 2, White considers the nRg5 to be white. Therefore, it can capture black pieces. It can also take neutral pieces, declaring them black for that purpose. As a further consequence, it controls certain squares like f5 in the second variation. Of course, after White has moved, Black could declare that neutral rook as black. But, looking again at the second variation, Kf5 is not a legal defense. White would again declare the nR as white. Dawson even says White must consider that he is giving check! This shows a general rule: a king may not put himself in check by a neutral piece.
The last two variations show that a neutral piece can be pinned by another.